Trying to simulate a Quantum System on a classical Turing Machine is not possible (see Feynman’s Papers below).

Enter David Deustch

Deutsch proposed the first design for a computer that operated quantum mechanically. The building block circuits were all designed as quantum circuits.

David Papers on Quantum Computing

The Universal Quantum Computer

Feynman’s Papers on Computation

1. 1960: There’s Plenty of Room at the Bottom.
   https://resolver.caltech.edu/CaltechES:23.5.1960Bottom
2. 1982: Simulating physics with computers.
   https://doi.org/10.1007/BF02650179
3. 1985: Quantum Mechanical Computers.
   https://www.optica-opn.org/home/articles/on/volume_11/issue_2/features/quantum_mechanical_computers/

Turing Machines

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If you have a Computer Science background, you may be aware that truly (100% ) random numbers simply do not exist. Random number generation algorithms using classical computers are at, best, reducing the chance of a collision.

Enter Quantum Randomness

While there are several algorithms that can be solved FASTER using quantum computers, there are certain operations that ONLY quantum computers can do. That is, classical computers, cannot, even in principle, perform such operations. One such example is a pure random number generation.

Quantum Randomness

A unitary operator like

when acting on a stationary state (such as

(1)  

)

can place that state into a superposition state (superposition of two states).
This superposition state, when measured, will with PERFECT RANDOMNESS, provide you with a

(2)  

or a

(3)  

output.

How exactly is a quantum computer implemented?

Imagine a row of atoms aligned in  magnetic field. Imagine this row being bombarded by a light wave. Each atom behaves slightly differently to the incoming wave – and either flips it’s axis – or stays unflipped.

The emerging light wave will contain information about which atoms flipped, and which didn’t.

In effect, this is a quantum calculation. We have an input (the initial state of the row of atoms). And we have an output (the final state, as deciphered from the exiting light wave).

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A given quantum memory register  (RAM) , may contain the output of your operation. A careful sampling from this quantum RAM, may contain the correct answer. Odds are overwhelming that it will NOT.  In fact, there are many more possible non solutions than there are solutions (to just about any problem that is solved using quantum parallelism – i.e. quantum superposition.)

What is needed is that a lot of the non solutions interfere with each other and disappear. And also, for the actual solutions to constructively interfere and amplify the amplitude. For this to happen, the problem has to lend itself to such a co-operative interference of amplitudes.

Shor’s Algorithm, devised by Peter Shor of AT&T, is one such problem.  More on this in another post.

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